I suspect that if detector-collector found some goodies in a random farm field, that there was probably something going on there, besides mere cultivation. Just as azsh07 says: It depends on if something were going on there , or very close by anyhow. Like a tavern, camp spot, battle spot, or ..... whatever.
Because if it's just "random farm fields", then no, they are typically a poor choice. You will go LOOONGGG between good coin finds, if you're angling for random fumble fingers losses of those who worked the field-labor. Ie.: planting, harvesting, etc.... (in the era before mechanization now means that hardly any foot traffic goes on in some crops, doh!).
Perhaps in Europe, where there's been continuous cultivation of the same fields for 1000 or 2000 years (95% of that hand-work before the modern era of mechanization), then yes: In countries that old, you can go out to "any random farm field" and find coins, buttons, etc... But here in the USA, we just haven't had the history and amount of time to make that "random" hunting worthwhile, IMHO. So we USA hunters study to find out where old habitations/homes were, stage stops, camps, parks, or ...... SOMETHING that brought foot-traffic, commerce ($$ changing hands), is always the best places to detect.
This really hit home at a place here in CA that is now just lettuce& brocolli fields near me. In the 1790s to 1820s, it had been the site of a contact era indian rancheria. But by the 1820s, it dwindled and was abandoned. Then starting in about the 1920s or so, it became row crops, and remains so to this day. Naturally, when we detect there, we're angling for Spanish reales and buttons, right ? But yes: An occasional nuisance wheatie or buffalo nickel, and one time even a silver washington quarter surfaced. Those were obviously modern field worker losses. But it occurred to me, that we had put in 100's of hours hunting this field, over 15+ yrs. , each fallow time. And while, yes, an occasional wheatie or clad turns up, yet it would NOT have been worth it to have worked these fields, if those were our goal. Even on the east coast, where admittedly fields have been cultivated 100 or 200 yrs. longer, it still seems to me that you're much better off angling where something , like a structure/home, saloon, stage stop, trading post, etc.... had been .